Fix mixed up column count of rhs (n) and original matrix (k)

* add input parameter tests
* revert check of n when it denotes the column of the matrix to be updated
  and correct the docs
* relax constraint on mb and update docs - special cases outside of the docs
  are handled by a call to GEQRT

SRC/clamtsqr.f

@@ -25,7 +25,7 @@
 *>                 SIDE = 'L'     SIDE = 'R'
 *> TRANS = 'N':      Q * C          C * Q
 *> TRANS = 'C':      Q**H * C       C * Q**H
-*>      where Q is a real orthogonal matrix defined as the product
+*>      where Q is a complex unitary matrix defined as the product
 *>      of blocked elementary reflectors computed by tall skinny
 *>      QR factorization (CLATSQR)
 *> \endverbatim
@@ -56,15 +56,14 @@
 *> \param[in] N
 *> \verbatim
 *>          N is INTEGER
-*>          The number of columns of the matrix C. M >= N >= 0.
+*>          The number of columns of the matrix C. N >= 0.
 *> \endverbatim
 *>
 *> \param[in] K
 *> \verbatim
 *>          K is INTEGER
 *>          The number of elementary reflectors whose product defines
-*>          the matrix Q.
-*>          N >= K >= 0;
+*>          the matrix Q. M >= K >= 0;
 *>
 *> \endverbatim
 *>
@@ -164,8 +163,8 @@
 *  =====================
 *>
 *> \verbatim
-*> Tall-Skinny QR (TSQR) performs QR by a sequence of orthogonal transformations,
-*> representing Q as a product of other orthogonal matrices
+*> Tall-Skinny QR (TSQR) performs QR by a sequence of unitary transformations,
+*> representing Q as a product of other unitary matrices
 *>   Q = Q(1) * Q(2) * . . . * Q(k)
 *> where each Q(i) zeros out subdiagonal entries of a block of MB rows of A:
 *>   Q(1) zeros out the subdiagonal entries of rows 1:MB of A
@@ -244,12 +243,12 @@ SUBROUTINE CLAMTSQR( SIDE, TRANS, M, N, K, MB, NB, A, LDA, T,
          INFO = -1
       ELSE IF( .NOT.TRAN .AND. .NOT.NOTRAN ) THEN
          INFO = -2
+      ELSE IF( M.LT.K ) THEN
+        INFO = -3
+      ELSE IF( N.LT.0 ) THEN
+        INFO = -4
       ELSE IF( K.LT.0 ) THEN
         INFO = -5
-      ELSE IF( N.LT.K ) THEN
-        INFO = -4
-      ELSE IF( M.LT.N ) THEN
-        INFO = -3
       ELSE IF( K.LT.NB .OR. NB.LT.1 ) THEN
         INFO = -7
       ELSE IF( LDA.LT.MAX( 1, Q ) ) THEN

SRC/clatsqr.f

@@ -202,12 +202,12 @@ SUBROUTINE CLATSQR( M, N, MB, NB, A, LDA, T, LDT, WORK,
         INFO = -1
       ELSE IF( N.LT.0 .OR. M.LT.N ) THEN
         INFO = -2
-      ELSE IF( MB.LE.N ) THEN
+      ELSE IF( MB.LT.1 ) THEN
         INFO = -3
       ELSE IF( NB.LT.1 .OR. ( NB.GT.N .AND. N.GT.0 )) THEN
         INFO = -4
       ELSE IF( LDA.LT.MAX( 1, M ) ) THEN
-        INFO = -5
+        INFO = -6
       ELSE IF( LDT.LT.NB ) THEN
         INFO = -8
       ELSE IF( LWORK.LT.(N*NB) .AND. (.NOT.LQUERY) ) THEN

SRC/dlamtsqr.f

@@ -56,15 +56,14 @@
 *> \param[in] N
 *> \verbatim
 *>          N is INTEGER
-*>          The number of columns of the matrix C. M >= N >= 0.
+*>          The number of columns of the matrix C. N >= 0.
 *> \endverbatim
 *>
 *> \param[in] K
 *> \verbatim
 *>          K is INTEGER
 *>          The number of elementary reflectors whose product defines
-*>          the matrix Q.
-*>          N >= K >= 0;
+*>          the matrix Q. M >= K >= 0;
 *>
 *> \endverbatim
 *>
@@ -244,12 +243,12 @@ SUBROUTINE DLAMTSQR( SIDE, TRANS, M, N, K, MB, NB, A, LDA, T,
          INFO = -1
       ELSE IF( .NOT.TRAN .AND. .NOT.NOTRAN ) THEN
          INFO = -2
+      ELSE IF( M.LT.K ) THEN
+        INFO = -3
+      ELSE IF( N.LT.0 ) THEN
+        INFO = -4
       ELSE IF( K.LT.0 ) THEN
         INFO = -5
-      ELSE IF( N.LT.K ) THEN
-        INFO = -4
-      ELSE IF( M.LT.N ) THEN
-        INFO = -3
       ELSE IF( K.LT.NB .OR. NB.LT.1 ) THEN
         INFO = -7
       ELSE IF( LDA.LT.MAX( 1, Q ) ) THEN

SRC/dlatsqr.f

@@ -57,7 +57,7 @@
 *> \verbatim
 *>          MB is INTEGER
 *>          The row block size to be used in the blocked QR.
-*>          MB > N.
+*>          MB > 0.
 *> \endverbatim
 *>
 *> \param[in] NB
@@ -202,12 +202,12 @@ SUBROUTINE DLATSQR( M, N, MB, NB, A, LDA, T, LDT, WORK,
         INFO = -1
       ELSE IF( N.LT.0 .OR. M.LT.N ) THEN
         INFO = -2
-      ELSE IF( MB.LE.N ) THEN
+      ELSE IF( MB.LT.1 ) THEN
         INFO = -3
       ELSE IF( NB.LT.1 .OR. ( NB.GT.N .AND. N.GT.0 )) THEN
         INFO = -4
       ELSE IF( LDA.LT.MAX( 1, M ) ) THEN
-        INFO = -5
+        INFO = -6
       ELSE IF( LDT.LT.NB ) THEN
         INFO = -8
       ELSE IF( LWORK.LT.(N*NB) .AND. (.NOT.LQUERY) ) THEN

SRC/slamtsqr.f

@@ -56,15 +56,14 @@
 *> \param[in] N
 *> \verbatim
 *>          N is INTEGER
-*>          The number of columns of the matrix C. M >= N >= 0.
+*>          The number of columns of the matrix C. N >= 0.
 *> \endverbatim
 *>
 *> \param[in] K
 *> \verbatim
 *>          K is INTEGER
 *>          The number of elementary reflectors whose product defines
-*>          the matrix Q.
-*>          N >= K >= 0;
+*>          the matrix Q. M >= K >= 0;
 *>
 *> \endverbatim
 *>
@@ -244,12 +243,12 @@ SUBROUTINE SLAMTSQR( SIDE, TRANS, M, N, K, MB, NB, A, LDA, T,
          INFO = -1
       ELSE IF( .NOT.TRAN .AND. .NOT.NOTRAN ) THEN
          INFO = -2
+      ELSE IF( M.LT.K ) THEN
+        INFO = -3
+      ELSE IF( N.LT.0 ) THEN
+        INFO = -4
       ELSE IF( K.LT.0 ) THEN
         INFO = -5
-      ELSE IF( N.LT.K ) THEN
-        INFO = -4
-      ELSE IF( M.LT.N ) THEN
-        INFO = -3
       ELSE IF( K.LT.NB .OR. NB.LT.1 ) THEN
         INFO = -7
       ELSE IF( LDA.LT.MAX( 1, Q ) ) THEN

SRC/slatsqr.f

@@ -202,12 +202,12 @@ SUBROUTINE SLATSQR( M, N, MB, NB, A, LDA, T, LDT, WORK,
         INFO = -1
       ELSE IF( N.LT.0 .OR. M.LT.N ) THEN
         INFO = -2
-      ELSE IF( MB.LE.N ) THEN
+      ELSE IF( MB.LT.1 ) THEN
         INFO = -3
       ELSE IF( NB.LT.1 .OR. ( NB.GT.N .AND. N.GT.0 )) THEN
         INFO = -4
       ELSE IF( LDA.LT.MAX( 1, M ) ) THEN
-        INFO = -5
+        INFO = -6
       ELSE IF( LDT.LT.NB ) THEN
         INFO = -8
       ELSE IF( LWORK.LT.(N*NB) .AND. (.NOT.LQUERY) ) THEN

SRC/zlamtsqr.f

@@ -25,7 +25,7 @@
 *>                 SIDE = 'L'     SIDE = 'R'
 *> TRANS = 'N':      Q * C          C * Q
 *> TRANS = 'C':      Q**H * C       C * Q**H
-*>      where Q is a real orthogonal matrix defined as the product
+*>      where Q is a complex unitary matrix defined as the product
 *>      of blocked elementary reflectors computed by tall skinny
 *>      QR factorization (ZLATSQR)
 *> \endverbatim
@@ -56,15 +56,14 @@
 *> \param[in] N
 *> \verbatim
 *>          N is INTEGER
-*>          The number of columns of the matrix C. M >= N >= 0.
+*>          The number of columns of the matrix C. N >= 0.
 *> \endverbatim
 *>
 *> \param[in] K
 *> \verbatim
 *>          K is INTEGER
 *>          The number of elementary reflectors whose product defines
-*>          the matrix Q.
-*>          N >= K >= 0;
+*>          the matrix Q. M >= K >= 0;
 *>
 *> \endverbatim
 *>
@@ -164,8 +163,8 @@
 *  =====================
 *>
 *> \verbatim
-*> Tall-Skinny QR (TSQR) performs QR by a sequence of orthogonal transformations,
-*> representing Q as a product of other orthogonal matrices
+*> Tall-Skinny QR (TSQR) performs QR by a sequence of unitary transformations,
+*> representing Q as a product of other unitary matrices
 *>   Q = Q(1) * Q(2) * . . . * Q(k)
 *> where each Q(i) zeros out subdiagonal entries of a block of MB rows of A:
 *>   Q(1) zeros out the subdiagonal entries of rows 1:MB of A
@@ -244,12 +243,12 @@ SUBROUTINE ZLAMTSQR( SIDE, TRANS, M, N, K, MB, NB, A, LDA, T,
          INFO = -1
       ELSE IF( .NOT.TRAN .AND. .NOT.NOTRAN ) THEN
          INFO = -2
+      ELSE IF( M.LT.K ) THEN
+        INFO = -3
+      ELSE IF( N.LT.0 ) THEN
+        INFO = -4
       ELSE IF( K.LT.0 ) THEN
         INFO = -5
-      ELSE IF( N.LT.K ) THEN
-        INFO = -4
-      ELSE IF( M.LT.N ) THEN
-        INFO = -3
       ELSE IF( K.LT.NB .OR. NB.LT.1 ) THEN
         INFO = -7
       ELSE IF( LDA.LT.MAX( 1, Q ) ) THEN

SRC/zlatsqr.f

@@ -202,12 +202,12 @@ SUBROUTINE ZLATSQR( M, N, MB, NB, A, LDA, T, LDT, WORK,
         INFO = -1
       ELSE IF( N.LT.0 .OR. M.LT.N ) THEN
         INFO = -2
-      ELSE IF( MB.LE.N ) THEN
+      ELSE IF( MB.LT.1 ) THEN
         INFO = -3
       ELSE IF( NB.LT.1 .OR. ( NB.GT.N .AND. N.GT.0 )) THEN
         INFO = -4
       ELSE IF( LDA.LT.MAX( 1, M ) ) THEN
-        INFO = -5
+        INFO = -6
       ELSE IF( LDT.LT.NB ) THEN
         INFO = -8
       ELSE IF( LWORK.LT.(N*NB) .AND. (.NOT.LQUERY) ) THEN

TESTING/LIN/cerrtsqr.f

@@ -70,7 +70,7 @@ SUBROUTINE CERRTSQR( PATH, NUNIT )
       PARAMETER          ( NMAX = 2 )
 *     ..
 *     .. Local Scalars ..
-      INTEGER            I, INFO, J, NB
+      INTEGER            I, INFO, J, MB, NB
 *     ..
 *     .. Local Arrays ..
       COMPLEX            A( NMAX, NMAX ), T( NMAX, NMAX ), W( NMAX ),
@@ -130,6 +130,35 @@ SUBROUTINE CERRTSQR( PATH, NUNIT )
       CALL CGEQR( 3, 2, A, 3, TAU, 8, W, 0, INFO )
       CALL CHKXER( 'CGEQR', INFOT, NOUT, LERR, OK )
 *
+*     CLATSQR
+*
+      MB = 1
+      NB = 1
+      SRNAMT = 'CLATSQR'
+      INFOT = 1
+      CALL CLATSQR( -1, 0, MB, NB, A, 1, TAU, 1, W, 1, INFO )
+      CALL CHKXER( 'CLATSQR', INFOT, NOUT, LERR, OK )
+      INFOT = 2
+      CALL CLATSQR( 1, 2, MB, NB, A, 1, TAU, 1, W, 1, INFO )
+      CALL CHKXER( 'CLATSQR', INFOT, NOUT, LERR, OK )
+      CALL CLATSQR( 0, -1, MB, NB, A, 1, TAU, 1, W, 1, INFO )
+      CALL CHKXER( 'CLATSQR', INFOT, NOUT, LERR, OK )
+      INFOT = 3
+      CALL CLATSQR( 2, 1, -1, NB, A, 2, TAU, 1, W, 1, INFO )
+      CALL CHKXER( 'CLATSQR', INFOT, NOUT, LERR, OK )
+      INFOT = 4
+      CALL CLATSQR( 2, 1, MB, 2, A, 2, TAU, 1, W, 1, INFO )
+      CALL CHKXER( 'CLATSQR', INFOT, NOUT, LERR, OK )
+      INFOT = 6
+      CALL CLATSQR( 2, 1, MB, NB, A, 1, TAU, 1, W, 1, INFO )
+      CALL CHKXER( 'CLATSQR', INFOT, NOUT, LERR, OK )
+      INFOT = 8
+      CALL CLATSQR( 2, 1, MB, NB, A, 2, TAU, 0, W, 1, INFO )
+      CALL CHKXER( 'CLATSQR', INFOT, NOUT, LERR, OK )
+      INFOT = 10
+      CALL CLATSQR( 2, 1, MB, NB, A, 2, TAU, 2, W, 0, INFO )
+      CALL CHKXER( 'CLATSQR', INFOT, NOUT, LERR, OK )
+*
 *     CGEMQR
 *
       TAU(1)=1

TESTING/LIN/derrtsqr.f

@@ -70,7 +70,7 @@ SUBROUTINE DERRTSQR( PATH, NUNIT )
       PARAMETER          ( NMAX = 2 )
 *     ..
 *     .. Local Scalars ..
-      INTEGER            I, INFO, J, NB
+      INTEGER            I, INFO, J, MB, NB
 *     ..
 *     .. Local Arrays ..
       DOUBLE PRECISION   A( NMAX, NMAX ), T( NMAX, NMAX ), W( NMAX ),
@@ -130,6 +130,35 @@ SUBROUTINE DERRTSQR( PATH, NUNIT )
       CALL DGEQR( 3, 2, A, 3, TAU, 7, W, 0, INFO )
       CALL CHKXER( 'DGEQR', INFOT, NOUT, LERR, OK )
 *
+*     DLATSQR
+*
+      MB = 1
+      NB = 1
+      SRNAMT = 'DLATSQR'
+      INFOT = 1
+      CALL DLATSQR( -1, 0, MB, NB, A, 1, TAU, 1, W, 1, INFO )
+      CALL CHKXER( 'DLATSQR', INFOT, NOUT, LERR, OK )
+      INFOT = 2
+      CALL DLATSQR( 1, 2, MB, NB, A, 1, TAU, 1, W, 1, INFO )
+      CALL CHKXER( 'DLATSQR', INFOT, NOUT, LERR, OK )
+      CALL DLATSQR( 0, -1, MB, NB, A, 1, TAU, 1, W, 1, INFO )
+      CALL CHKXER( 'DLATSQR', INFOT, NOUT, LERR, OK )
+      INFOT = 3
+      CALL DLATSQR( 2, 1, -1, NB, A, 2, TAU, 1, W, 1, INFO )
+      CALL CHKXER( 'DLATSQR', INFOT, NOUT, LERR, OK )
+      INFOT = 4
+      CALL DLATSQR( 2, 1, MB, 2, A, 2, TAU, 1, W, 1, INFO )
+      CALL CHKXER( 'DLATSQR', INFOT, NOUT, LERR, OK )
+      INFOT = 6
+      CALL DLATSQR( 2, 1, MB, NB, A, 1, TAU, 1, W, 1, INFO )
+      CALL CHKXER( 'DLATSQR', INFOT, NOUT, LERR, OK )
+      INFOT = 8
+      CALL DLATSQR( 2, 1, MB, NB, A, 2, TAU, 0, W, 1, INFO )
+      CALL CHKXER( 'DLATSQR', INFOT, NOUT, LERR, OK )
+      INFOT = 10
+      CALL DLATSQR( 2, 1, MB, NB, A, 2, TAU, 2, W, 0, INFO )
+      CALL CHKXER( 'DLATSQR', INFOT, NOUT, LERR, OK )
+*
 *     DGEMQR
 *
       TAU(1)=1

TESTING/LIN/serrtsqr.f

@@ -70,7 +70,7 @@ SUBROUTINE SERRTSQR( PATH, NUNIT )
       PARAMETER          ( NMAX = 2 )
 *     ..
 *     .. Local Scalars ..
-      INTEGER            I, INFO, J, NB
+      INTEGER            I, INFO, J, MB, NB
 *     ..
 *     .. Local Arrays ..
       REAL               A( NMAX, NMAX ), T( NMAX, NMAX ), W( NMAX ),
@@ -130,6 +130,35 @@ SUBROUTINE SERRTSQR( PATH, NUNIT )
       CALL SGEQR( 3, 2, A, 3, TAU, 7, W, 0, INFO )
       CALL CHKXER( 'SGEQR', INFOT, NOUT, LERR, OK )
 *
+*     SLATSQR
+*
+      MB = 1
+      NB = 1
+      SRNAMT = 'SLATSQR'
+      INFOT = 1
+      CALL SLATSQR( -1, 0, MB, NB, A, 1, TAU, 1, W, 1, INFO )
+      CALL CHKXER( 'SLATSQR', INFOT, NOUT, LERR, OK )
+      INFOT = 2
+      CALL SLATSQR( 1, 2, MB, NB, A, 1, TAU, 1, W, 1, INFO )
+      CALL CHKXER( 'SLATSQR', INFOT, NOUT, LERR, OK )
+      CALL SLATSQR( 0, -1, MB, NB, A, 1, TAU, 1, W, 1, INFO )
+      CALL CHKXER( 'SLATSQR', INFOT, NOUT, LERR, OK )
+      INFOT = 3
+      CALL SLATSQR( 2, 1, -1, NB, A, 2, TAU, 1, W, 1, INFO )
+      CALL CHKXER( 'SLATSQR', INFOT, NOUT, LERR, OK )
+      INFOT = 4
+      CALL SLATSQR( 2, 1, MB, 2, A, 2, TAU, 1, W, 1, INFO )
+      CALL CHKXER( 'SLATSQR', INFOT, NOUT, LERR, OK )
+      INFOT = 6
+      CALL SLATSQR( 2, 1, MB, NB, A, 1, TAU, 1, W, 1, INFO )
+      CALL CHKXER( 'SLATSQR', INFOT, NOUT, LERR, OK )
+      INFOT = 8
+      CALL SLATSQR( 2, 1, MB, NB, A, 2, TAU, 0, W, 1, INFO )
+      CALL CHKXER( 'SLATSQR', INFOT, NOUT, LERR, OK )
+      INFOT = 10
+      CALL SLATSQR( 2, 1, MB, NB, A, 2, TAU, 2, W, 0, INFO )
+      CALL CHKXER( 'SLATSQR', INFOT, NOUT, LERR, OK )
+*
 *     SGEMQR
 *
       TAU(1)=1